Simplify; express your answer in exponential form. Assume $x\neq 0, q\neq 0$. $\dfrac{{(x^{-1})^{5}}}{{(x^{-4}q^{-4})^{-1}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{-1}}$ to the exponent ${5}$ . Now ${-1 \times 5 = -5}$ , so ${(x^{-1})^{5} = x^{-5}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-4}q^{-4})^{-1} = (x^{-4})^{-1}(q^{-4})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{-1})^{5}}}{{(x^{-4}q^{-4})^{-1}}} = \dfrac{{x^{-5}}}{{x^{4}q^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{-5}}}{{x^{4}q^{4}}} = \dfrac{{x^{-5}}}{{x^{4}}} \cdot \dfrac{{1}}{{q^{4}}} = x^{{-5} - {4}} \cdot q^{- {4}} = x^{-9}q^{-4}$.